I need some help on following question. Any help is greatly appreciated.
Let $p$ be a sigma finite measure on measurable space $( [0,1], M )$ where $M$ is the sigma algebra of Lebesgue measurable subsets of $[0,1]$. For $x$ in $[0,1]$, define $F(x) = p ([0,x])$.
Show that $p$ is absolutely continuous with respect to Lebesgue measure $m$ on $[0,1]$ iff $F$ is an absolutely continuous function on $[0,1]$ satisfying $F(0) = 0$.